Add an image import button in addon
You can get access to the file browser in Blender by using the StringProperty with the subtype "FILE_PATH". As documented here. And example of using this would be 

file_path = StringProperty(name = "File", subtype = "FILE_PATH")


Then you can just use file_path like this:

bpy.data.images.load(file_path) #most of the time you will have to do self.file_path


If you need to use that image elsewhere just set all that equal to a variable.